Airfoil shape for a compressor

ABSTRACT

An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in a scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

RELATED APPLICATIONS

The present application is related to the following commonly assigned applications: Ser. No. ______ (Docket No. 277754 (1013)); Ser. No. ______ (Docket No. 277765 (1014)); Ser. No. ______ (Docket No. 277784 (1012)); Ser. No. ______ (Docket No. 277913 (1016)); Ser. No. ______ (Docket No. 278957 (1015)); Ser. No. ______ (Docket No. 278976 (1017)); Ser. No. ______ (Docket No. 279003 (1018)); Ser. No. ______ (Docket No. 279149 (1019)); Ser. No. ______ (Docket No. 280088 (1020)); Ser. No. ______ (Docket No. 280098 (1021)), filed concurrently herewith.

TECHNICAL FIELD

The present application and the resultant patent relate generally to gas turbine engines and more particularly relates to an airfoil profile or airfoil shape for use in a compressor.

BACKGROUND OF THE INVENTION

In a gas turbine engine, many system requirements should be met at each stage of the flow path therethrough to meet design goals. These design goals include, but are not limited to, overall improved efficiency, a reduction in vibratory response, improved airfoil loading capability, and the like. For example, a compressor airfoil profile should achieve thermal and mechanical operating requirements for a particular stage in the compressor. Moreover, component lifetime, reliability, and cost targets also should be met.

SUMMARY OF THE INVENTION

According to one aspect of the present application, an article of manufacture is provided with a nominal airfoil profile substantially in accordance with the Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.

According to another aspect of the present application, an article of manufacture is provided with a suction-side nominal airfoil profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined smoothly with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.

According to yet another aspect of the present application, a compressor is provided with a number of rotor blades, each of the rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with the suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.

These and other features and improvements of the present application and the resultant patent will become apparent to one of ordinary skill in the art upon review of the following detailed description when taken in conjunction with the several drawings and the appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a gas turbine engine including a compressor, a combustor, a turbine, and a load.

FIG. 2 is a schematic diagram of a compressor with multiple stages and a flow path therethrough.

FIG. 3 is a perspective view of a rotor blade airfoil as may be described herein.

FIG. 4 is a cross-sectional view of the rotor blade airfoil taken along line 4-4 of FIG. 3.

DETAILED DESCRIPTION

Referring now to the drawings, in which like numerals refer to like elements throughout the several views, FIG. 1 shows a schematic view of gas turbine engine 10 as may be used herein. The gas turbine engine 10 may include a compressor 15. The compressor 15 compresses an incoming flow of air 20. The compressor 15 delivers the compressed flow of air 20 to a combustor 25. The combustor 25 mixes the compressed flow of air 20 with a pressurized flow of fuel 30 and ignites the mixture to create a flow of combustion gases 35. Although only a single combustor 25 is shown, the gas turbine engine 10 may include any number of the combustors 25 arranged in a circumferential array or otherwise. The flow of combustion gases 35 is delivered in turn to a turbine 40. The flow of combustion gases 35 drives the turbine 40 so as to produce mechanical work. The mechanical work produced in the turbine 40 drives the compressor 15 via a shaft 45 and an external load 50 such as an electrical generator and the like.

The gas turbine engine 10 may use natural gas, liquid fuels, various types of syngas, and/or other types of fuels and blends thereof. The gas turbine engine 10 may be any one of a number of different gas turbine engines offered by General Electric Company of Schenectady, New York, including, but not limited to, those such as a 7 or a 9 series heavy duty gas turbine engine and the like. The gas turbine engine 10 may have different configurations and may use other types of components. Other types of gas turbine engines also may be used herein. Multiple gas turbine engines, other types of turbines, and other types of power generation equipment also may be used herein together.

FIG. 2 shows an example of the compressor 15. The compressor 15 may include a number of compressor stages with an axial compressor flow path 55 therethrough. As one non-limiting example only, the compressor flow path 55 may include about eighteen rotor/stator stages. The exact number of rotor and stator stages, however, may be a matter of engineering design choice and may be more or less than the illustrated eighteen stages. It is to be understood that any number of rotor and stator stages may be provided herein.

Each stage of the compressor 15 may include a number of circumferentially spaced rotor blades 60 mounted on a rotor wheel 65 and a number of circumferentially spaced stator vanes 70 attached to a static compressor case 75. Each of the rotor wheels 65 may be attached to an aft drive shaft 80, which may be connected to the turbine section of the engine. The rotor blades and stator vanes may lie in the flow path 55 of the compressor 15. The direction of airflow through the compressor flow path 55 flows generally from left to right in FIG. 2. Other components and other configurations may be used herein.

The compressor rotor blades 60 impart kinetic energy to the airflow and therefore bring about a desired pressure rise. Directly following the rotor blades 60 may be a stage of the compressor stator vanes 70. However, in some designs the stator vanes may precede the rotor blades. Both the rotor blades and stator vanes turn the airflow, slow the airflow velocity (in the respective airfoil frame of reference), and yield a rise in the static pressure of the airflow. Typically, multiple rows of rotor/stator stages are arranged in axial flow compressors to achieve a desired discharge to inlet pressure ratio. Each rotor blade and stator vane includes an airfoil, and these airfoils can be secured to rotor wheels or a stator case by an appropriate attachment configuration, often known as a “root,” “base” or “dovetail”. In addition, the compressor 15 also may include inlet guide vanes (IGV's) 85, variable stator vanes (VSV's) 90, and exit or exhaust guide vanes (EGV's) 95. All of these blades and vanes have airfoils that act on the medium (e.g., air) passing through the compressor flow path 55. Other components and other configurations may be used herein.

The rotor blades 60 and stator vanes 70 are merely exemplary of the stages of the compressor 15 described herein. In addition, each rotor blade 60, stator vane 70, inlet guide vane 85, variable stator vane 90, and exit guide vane 95 may be considered an article of manufacture. Further, the article of manufacture may include a rotor blade configured for use with a compressor 15.

FIG. 3 shows an example of a rotor blade 100 as may be described herein. In this example, the rotor blade 100 includes an airfoil 105. Each of the rotor blades 100 may have an airfoil profile at any cross-section from an airfoil root 110 to an airfoil tip 120. The airfoil 105 may connect to a mounting base 130, which also may be referred to as a dovetail. The mounting base 130 fits into a complementary shaped groove or slot in the rotor or rotor wheel 65. Examples of the compressor 15 may include a variety of blades 60 and vanes 70, 85, 90, 95 arranged in multiple stages.

Referring to FIG. 4, the airfoil 105 may have a suction side 140 and a pressure side 150. The suction side 140 may be located on the opposing side of the airfoil 105 from the pressure side 150. Thus, each rotor blade 60 may have an airfoil profile at any cross-section in the shape of the airfoil 105. The airfoil 105 also may include a leading edge 160 and a trailing edge 170 and with a chord length 180 extending therebetween. The root 110 of the airfoil 105 corresponds to the lowest non-dimensional Z value of scalable TABLE 1. The tip 120 of the airfoil 105 corresponds to the highest non-dimensional Z value of scalable TABLE 1. An airfoil 105 may extend beyond the compressor flowpath and may be tipped to achieve the desired endwall clearances. By way of example only, the airfoil may have a height from about one (1) inch to about twenty (20) inches (about 2.54 centimeters to about 50.8 centimeters) or more. Any specific airfoil height may be used herein as desired in a specific application. Other components and other configurations may be used herein.

The compressor flow path 55 requires airfoils 105 that meet system requirements of aerodynamic and mechanical blade/vane loading and efficiency. For example, it is desirable that the airfoils 105 are designed to reduce the vibratory response or vibratory stress response of the respective blades and/or vanes. Materials such as high strength alloys, non-corrosive alloys, and/or stainless steels may be used in the blades and/or vanes. To define the airfoil shape of each blade airfoil and/or vane airfoil, there is a unique set or loci of points in space that meet the stage requirements and can be manufactured. These unique loci of points meet the requirements for stage efficiency and may be arrived at by iteration between aerodynamic and mechanical loadings so as to enable the turbine and compressor to run in an efficient, safe, reliable, and smooth manner. These points are unique and specific to the system. The locus that defines the airfoil profile includes a set of points with X, Y, and Z coordinates relative to a reference origin coordinate system. The three-dimensional Cartesian coordinate system of X, Y, and Z values given in scalable TABLE 1 below defines the profile of the rotor blade airfoil at various locations along its length. The scalable TABLE 1 lists data for a non-coated airfoil. The envelope/tolerance for the coordinates may be about +/−5% of the chord length 180 in a direction normal to any airfoil surface location or about +/−0.25 inches (about 6.36 millimeters) in a direction normal to any airfoil surface location. However, tolerances of about +/−0.15 inches to about +/−0.25 inches (about 6.36 millimeters), or about +/−3% to about +/−5% in a direction normal to an airfoil surface location may also be used, as desired in the specific application.

A point data origin 190 may be the mid-point of the suction or pressure side of the base or tip of the airfoil, the leading edge or trailing edge of the base of the airfoil, or any other suitable location as desired. The coordinate values for the X, Y, and Z coordinates are set forth in non-dimensionalized units in scalable TABLE 1, although other units of dimensions may be used when the values are appropriately converted. As one example only, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by a constant number (e.g., 100). The number, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, ¼, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.), a mixed number (e.g., 11/2, 101/4, etc.), and the like. The dimensional distances may be in any suitable format (e.g., inches, feet, millimeters, centimeters, meters, etc.) As one non-limiting example only, the Cartesian coordinate system has orthogonally-related X, Y, and Z axes and the X axis may lie generally parallel to the compressor rotor centerline, i.e., the rotary axis and a positive X coordinate value is axial toward the aft, i.e., exhaust end of the turbine. The positive Y coordinate value extends tangentially in the direction of rotation of the rotor and the positive Z coordinate value is radially outwardly toward the rotor blade tip or stator vane base. All the values in scalable TABLE 1 are given at room temperature and are unfilleted.

By defining X and Y coordinate values at selected locations in a Z direction (or height) normal to the X, Y plane, the profile section or airfoil shape of the airfoil, at each Z height along the length of the airfoil may be ascertained. By connecting the X and Y values with smooth continuing arcs, each profile section at each Z height may be fixed. The airfoil profiles of the various surface locations between each Z height may be determined by smoothly connecting the adjacent profile sections to one another to form the airfoil profile.

The values in TABLE 1 may be generated and shown from zero to four or more decimal places for determining the profile of the airfoil. As the airfoil heats up the associated stress and temperature may cause a change in the X, Y, and Z values. Accordingly, the values for the profile given in TABLE 1 represent ambient, non-operating or non-hot conditions (e.g., room temperature) and may be for an uncoated airfoil.

There are typical manufacturing tolerances as well as optional coatings which may be accounted for in the actual profile of the airfoil. Each section may be joined smoothly with the other sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in TABLE 1 below. Accordingly, a distance of about +/−5% of chord length and/or +/−0.25 inches (about 6.36 millimeters) in a direction normal to a surface location along the airfoil profile defines an airfoil profile envelope for this particular airfoil design and compressor, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in the TABLE 1 below at the same temperature. Additionally, a distance of about +/−5% of a chord length in a direction normal to an airfoil surface location along the airfoil profile also may define an airfoil profile envelope for this particular airfoil design. The data is scalable and the geometry pertains to all aerodynamic scales, at, above and/or below about 3,000 RPM. The rotor blade airfoil design is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The coordinate values given in scalable TABLE 1 below provide the nominal profile for exemplary stages of a compressor rotor blade. Specifically, a third stage rotor blade of, for example, a 7HA.01 or a 9HA.01 compressor and the like:

TABLE 1 Pressure Side Suction Side X Y Z X Y Z −1.8982 1.9618 −0.6298 2.2448 −1.2598 −0.6298 −1.8973 1.9623 −0.6298 2.2419 −1.2678 −0.6298 −1.8953 1.9634 −0.6298 2.2361 −1.2776 −0.6298 −1.8913 1.9649 −0.6298 2.2261 −1.2875 −0.6298 −1.8828 1.9668 −0.6298 2.2110 −1.2950 −0.6298 −1.8694 1.9666 −0.6298 2.1885 −1.2955 −0.6298 −1.8461 1.9600 −0.6298 2.1591 −1.2910 −0.6298 −1.8179 1.9447 −0.6298 2.1225 −1.2853 −0.6298 −1.7842 1.9187 −0.6298 2.0779 −1.2782 −0.6298 −1.7455 1.8818 −0.6298 2.0249 −1.2699 −0.6298 −1.6977 1.8316 −0.6298 1.9629 −1.2600 −0.6298 −1.6443 1.7721 −0.6298 1.8897 −1.2482 −0.6298 −1.5891 1.7071 −0.6298 1.8051 −1.2342 −0.6298 −1.5280 1.6329 −0.6298 1.7095 −1.2180 −0.6298 −1.4609 1.5500 −0.6298 1.6027 −1.1990 −0.6298 −1.3871 1.4587 −0.6298 1.4850 −1.1769 −0.6298 −1.3096 1.3636 −0.6298 1.3564 −1.1509 −0.6298 −1.2279 1.2650 −0.6298 1.2227 −1.1215 −0.6298 −1.1418 1.1631 −0.6298 1.0840 −1.0881 −0.6298 −1.0509 1.0583 −0.6298 0.9405 −1.0498 −0.6298 −0.9549 0.9511 −0.6298 0.7929 −1.0057 −0.6298 −0.8534 0.8415 −0.6298 0.6423 −0.9551 −0.6298 −0.7459 0.7303 −0.6298 0.4889 −0.8970 −0.6298 −0.6325 0.6175 −0.6298 0.3333 −0.8302 −0.6298 −0.5166 0.5072 −0.6298 0.1810 −0.7561 −0.6298 −0.3980 0.3998 −0.6298 0.0324 −0.6746 −0.6298 −0.2766 0.2954 −0.6298 −0.1125 −0.5850 −0.6298 −0.1523 0.1945 −0.6298 −0.2536 −0.4875 −0.6298 −0.0251 0.0972 −0.6298 −0.3899 −0.3832 −0.6298 0.1046 0.0033 −0.6298 −0.5208 −0.2736 −0.6298 0.2362 −0.0880 −0.6298 −0.6465 −0.1587 −0.6298 0.3689 −0.1774 −0.6298 −0.7671 −0.0388 −0.6298 0.5029 −0.2651 −0.6298 −0.8827 0.0861 −0.6298 0.6382 −0.3507 −0.6298 −0.9937 0.2157 −0.6298 0.7746 −0.4343 −0.6298 −1.1000 0.3500 −0.6298 0.9077 −0.5131 −0.6298 −1.1983 0.4838 −0.6298 1.0370 −0.5875 −0.6298 −1.2890 0.6160 −0.6298 1.1626 −0.6576 −0.6298 −1.3727 0.7459 −0.6298 1.2844 −0.7239 −0.6298 −1.4500 0.8731 −0.6298 1.4021 −0.7865 −0.6298 −1.5215 0.9972 −0.6298 1.5156 −0.8456 −0.6298 −1.5877 1.1176 −0.6298 1.6248 −0.9016 −0.6298 −1.6488 1.2344 −0.6298 1.7248 −0.9522 −0.6298 −1.7056 1.3469 −0.6298 1.8153 −0.9976 −0.6298 −1.7556 1.4500 −0.6298 1.8966 −1.0380 −0.6298 −1.7986 1.5438 −0.6298 1.9683 −1.0736 −0.6298 −1.8353 1.6278 −0.6298 2.0304 −1.1044 −0.6298 −1.8673 1.7075 −0.6298 2.0831 −1.1304 −0.6298 −1.8926 1.7777 −0.6298 2.1280 −1.1526 −0.6298 −1.9097 1.8323 −0.6298 2.1658 −1.1713 −0.6298 −1.9192 1.8771 −0.6298 2.1968 −1.1867 −0.6298 −1.9209 1.9115 −0.6298 2.2217 −1.1991 −0.6298 −1.9165 1.9368 −0.6298 2.2373 −1.2134 −0.6298 −1.9104 1.9497 −0.6298 2.2444 −1.2279 −0.6298 −1.9046 1.9569 −0.6298 2.2468 −1.2411 −0.6298 −1.9011 1.9599 −0.6298 2.2464 −1.2519 −0.6298 −1.8992 1.9611 −0.6298 −1.9245 1.8651 −0.2569 2.2559 −1.2572 −0.2569 −1.9236 1.8657 −0.2569 2.2528 −1.2650 −0.2569 −1.9217 1.8668 −0.2569 2.2468 −1.2743 −0.2569 −1.9178 1.8685 −0.2569 2.2365 −1.2837 −0.2569 −1.9095 1.8708 −0.2569 2.2211 −1.2902 −0.2569 −1.8962 1.8711 −0.2569 2.1988 −1.2898 −0.2569 −1.8728 1.8657 −0.2569 2.1698 −1.2851 −0.2569 −1.8440 1.8522 −0.2569 2.1337 −1.2790 −0.2569 −1.8091 1.8284 −0.2569 2.0898 −1.2716 −0.2569 −1.7686 1.7943 −0.2569 2.0375 −1.2628 −0.2569 −1.7182 1.7477 −0.2569 1.9763 −1.2522 −0.2569 −1.6620 1.6918 −0.2569 1.9041 −1.2397 −0.2569 −1.6036 1.6306 −0.2569 1.8208 −1.2249 −0.2569 −1.5391 1.5608 −0.2569 1.7265 −1.2075 −0.2569 −1.4681 1.4825 −0.2569 1.6213 −1.1874 −0.2569 −1.3900 1.3962 −0.2569 1.5054 −1.1640 −0.2569 −1.3080 1.3064 −0.2569 1.3787 −1.1366 −0.2569 −1.2220 1.2133 −0.2569 1.2470 −1.1060 −0.2569 −1.1313 1.1171 −0.2569 1.1104 −1.0712 −0.2569 −1.0359 1.0181 −0.2569 0.9691 −1.0317 −0.2569 −0.9354 0.9167 −0.2569 0.8238 −0.9868 −0.2569 −0.8298 0.8132 −0.2569 0.6752 −0.9356 −0.2569 −0.7184 0.7079 −0.2569 0.5239 −0.8774 −0.2569 −0.6016 0.6009 −0.2569 0.3702 −0.8113 −0.2569 −0.4829 0.4959 −0.2569 0.2196 −0.7388 −0.2569 −0.3620 0.3932 −0.2569 0.0724 −0.6595 −0.2569 −0.2391 0.2929 −0.2569 −0.0715 −0.5732 −0.2569 −0.1139 0.1956 −0.2569 −0.2119 −0.4799 −0.2569 0.0133 0.1010 −0.2569 −0.3490 −0.3800 −0.2569 0.1427 0.0091 −0.2569 −0.4820 −0.2747 −0.2569 0.2734 −0.0807 −0.2569 −0.6104 −0.1643 −0.2569 0.4050 −0.1691 −0.2569 −0.7345 −0.0488 −0.2569 0.5377 −0.2561 −0.2569 −0.8543 0.0716 −0.2569 0.6713 −0.3415 −0.2569 −0.9690 0.1958 −0.2569 0.8058 −0.4253 −0.2569 −1.0786 0.3234 −0.2569 0.9369 −0.5047 −0.2569 −1.1801 0.4500 −0.2569 1.0642 −0.5798 −0.2569 −1.2741 0.5749 −0.2569 1.1878 −0.6508 −0.2569 −1.3614 0.6977 −0.2569 1.3075 −0.7180 −0.2569 −1.4425 0.8180 −0.2569 1.4232 −0.7815 −0.2569 −1.5180 0.9353 −0.2569 1.5348 −0.8415 −0.2569 −1.5882 1.0495 −0.2569 1.6422 −0.8982 −0.2569 −1.6535 1.1603 −0.2569 1.7406 −0.9495 −0.2569 −1.7144 1.2674 −0.2569 1.8299 −0.9954 −0.2569 −1.7682 1.3659 −0.2569 1.9099 −1.0362 −0.2569 −1.8143 1.4561 −0.2569 1.9805 −1.0721 −0.2569 −1.8537 1.5373 −0.2569 2.0419 −1.1030 −0.2569 −1.8880 1.6149 −0.2569 2.0938 −1.1292 −0.2569 −1.9150 1.6834 −0.2569 2.1382 −1.1515 −0.2569 −1.9332 1.7370 −0.2569 2.1755 −1.1702 −0.2569 −1.9434 1.7811 −0.2569 2.2062 −1.1856 −0.2569 −1.9459 1.8148 −0.2569 2.2308 −1.1980 −0.2569 −1.9420 1.8400 −0.2569 2.2473 −1.2111 −0.2569 −1.9363 1.8528 −0.2569 2.2551 −1.2253 −0.2569 −1.9307 1.8601 −0.2569 2.2579 −1.2384 −0.2569 −1.9273 1.8632 −0.2569 2.2576 −1.2492 −0.2569 −1.9255 1.8645 −0.2569 −1.9428 1.8004 0.0000 2.2635 −1.2554 0.0000 −1.9420 1.8009 0.0000 2.2604 −1.2631 0.0000 −1.9401 1.8020 0.0000 2.2542 −1.2722 0.0000 −1.9362 1.8038 0.0000 2.2437 −1.2812 0.0000 −1.9280 1.8059 0.0000 2.2282 −1.2871 0.0000 −1.9148 1.8063 0.0000 2.2062 −1.2861 0.0000 −1.8916 1.8010 0.0000 2.1775 −1.2812 0.0000 −1.8628 1.7881 0.0000 2.1418 −1.2749 0.0000 −1.8272 1.7658 0.0000 2.0984 −1.2672 0.0000 −1.7855 1.7340 0.0000 2.0467 −1.2580 0.0000 −1.7331 1.6902 0.0000 1.9864 −1.2470 0.0000 −1.6744 1.6376 0.0000 1.9150 −1.2338 0.0000 −1.6136 1.5796 0.0000 1.8327 −1.2183 0.0000 −1.5462 1.5131 0.0000 1.7396 −1.2003 0.0000 −1.4721 1.4385 0.0000 1.6357 −1.1793 0.0000 −1.3911 1.3561 0.0000 1.5211 −1.1549 0.0000 −1.3061 1.2701 0.0000 1.3960 −1.1266 0.0000 −1.2171 1.1808 0.0000 1.2660 −1.0951 0.0000 −1.1236 1.0884 0.0000 1.1312 −1.0595 0.0000 −1.0254 0.9933 0.0000 0.9916 −1.0194 0.0000 −0.9224 0.8958 0.0000 0.8480 −0.9741 0.0000 −0.8141 0.7962 0.0000 0.7010 −0.9231 0.0000 −0.7005 0.6947 0.0000 0.5511 −0.8655 0.0000 −0.5815 0.5914 0.0000 0.3987 −0.8006 0.0000 −0.4610 0.4899 0.0000 0.2492 −0.7299 0.0000 −0.3389 0.3901 0.0000 0.1028 −0.6530 0.0000 −0.2151 0.2926 0.0000 −0.0402 −0.5695 0.0000 −0.0895 0.1972 0.0000 −0.1799 −0.4793 0.0000 0.0381 0.1045 0.0000 −0.3164 −0.3825 0.0000 0.1671 0.0139 0.0000 −0.4496 −0.2803 0.0000 0.2973 −0.0751 0.0000 −0.5786 −0.1736 0.0000 0.4282 −0.1630 0.0000 −0.7032 −0.0628 0.0000 0.5599 −0.2498 0.0000 −0.8234 0.0523 0.0000 0.6924 −0.3352 0.0000 −0.9396 0.1714 0.0000 0.8260 −0.4191 0.0000 −1.0518 0.2944 0.0000 0.9558 −0.4987 0.0000 −1.1568 0.4166 0.0000 1.0820 −0.5744 0.0000 −1.2552 0.5376 0.0000 1.2045 −0.6460 0.0000 −1.3474 0.6568 0.0000 1.3231 −0.7138 0.0000 −1.4338 0.7738 0.0000 1.4378 −0.7780 0.0000 −1.5144 0.8879 0.0000 1.5484 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−2.0006 1.6742 0.8310 2.2831 −1.2327 0.8310 −1.9976 1.6775 0.8310 2.2826 −1.2431 0.8310 −1.9959 1.6790 0.8310 −2.0006 1.6836 1.2343 2.2533 −1.2507 1.2343 −1.9997 1.6843 1.2343 2.2497 −1.2579 1.2343 −1.9980 1.6854 1.2343 2.2428 −1.2664 1.2343 −1.9943 1.6875 1.2343 2.2318 −1.2742 1.2343 −1.9863 1.6900 1.2343 2.2162 −1.2785 1.2343 −1.9731 1.6909 1.2343 2.1948 −1.2759 1.2343 −1.9500 1.6866 1.2343 2.1671 −1.2695 1.2343 −1.9210 1.6750 1.2343 2.1326 −1.2614 1.2343 −1.8847 1.6550 1.2343 2.0907 −1.2515 1.2343 −1.8413 1.6264 1.2343 2.0407 −1.2397 1.2343 −1.7862 1.5871 1.2343 1.9824 −1.2258 1.2343 −1.7238 1.5402 1.2343 1.9134 −1.2091 1.2343 −1.6583 1.4888 1.2343 1.8340 −1.1896 1.2343 −1.5854 1.4300 1.2343 1.7440 −1.1671 1.2343 −1.5051 1.3638 1.2343 1.6436 −1.1414 1.2343 −1.4165 1.2912 1.2343 1.5328 −1.1123 1.2343 −1.3236 1.2157 1.2343 1.4119 −1.0792 1.2343 −1.2262 1.1376 1.2343 1.2861 −1.0430 1.2343 −1.1244 1.0567 1.2343 1.1556 −1.0036 1.2343 −1.0180 0.9730 1.2343 1.0205 −0.9602 1.2343 −0.9072 0.8866 1.2343 0.8814 −0.9123 1.2343 −0.7917 0.7979 1.2343 0.7387 −0.8596 1.2343 −0.6712 0.7070 1.2343 0.5929 −0.8012 1.2343 −0.5459 0.6140 1.2343 0.4445 −0.7366 1.2343 −0.4200 0.5216 1.2343 0.2986 −0.6671 1.2343 −0.2940 0.4295 1.2343 0.1554 −0.5926 1.2343 −0.1674 0.3381 1.2343 0.0151 −0.5130 1.2343 −0.0401 0.2478 1.2343 −0.1224 −0.4277 1.2343 0.0877 0.1584 1.2343 −0.2569 −0.3372 1.2343 0.2161 0.0694 1.2343 −0.3891 −0.2421 1.2343 0.3445 −0.0194 1.2343 −0.5191 −0.1431 1.2343 0.4729 −0.1081 1.2343 −0.6468 −0.0403 1.2343 0.6017 −0.1963 1.2343 −0.7715 0.0656 1.2343 0.7309 −0.2839 1.2343 −0.8932 0.1752 1.2343 0.8607 −0.3706 1.2343 −1.0119 0.2880 1.2343 0.9869 −0.4534 1.2343 −1.1244 0.3995 1.2343 1.1093 −0.5323 1.2343 −1.2308 0.5093 1.2343 1.2279 −0.6075 1.2343 −1.3314 0.6171 1.2343 1.3427 −0.6791 1.2343 −1.4263 0.7227 1.2343 1.4536 −0.7470 1.2343 −1.5154 0.8263 1.2343 1.5607 −0.8114 1.2343 −1.5985 0.9276 1.2343 1.6636 −0.8723 1.2343 −1.6755 1.0270 1.2343 1.7580 −0.9274 1.2343 −1.7469 1.1237 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1.9941 −1.2511 1.6072 −1.7728 1.6050 1.6072 1.9364 −1.2366 1.6072 −1.7105 1.5590 1.6072 1.8682 −1.2192 1.6072 −1.6449 1.5088 1.6072 1.7896 −1.1989 1.6072 −1.5728 1.4501 1.6072 1.7008 −1.1754 1.6072 −1.4941 1.3831 1.6072 1.6017 −1.1485 1.6072 −1.4068 1.3102 1.6072 1.4923 −1.1178 1.6072 −1.3148 1.2350 1.6072 1.3730 −1.0829 1.6072 −1.2182 1.1572 1.6072 1.2491 −1.0446 1.6072 −1.1168 1.0770 1.6072 1.1206 −1.0026 1.6072 −1.0108 0.9944 1.6072 0.9877 −0.9566 1.6072 −0.9003 0.9092 1.6072 0.8508 −0.9058 1.6072 −0.7854 0.8214 1.6072 0.7107 −0.8500 1.6072 −0.6661 0.7307 1.6072 0.5676 −0.7887 1.6072 −0.5425 0.6371 1.6072 0.4220 −0.7210 1.6072 −0.4186 0.5438 1.6072 0.2788 −0.6488 1.6072 −0.2943 0.4510 1.6072 0.1384 −0.5720 1.6072 −0.1696 0.3591 1.6072 0.0008 −0.4903 1.6072 −0.0441 0.2679 1.6072 −0.1340 −0.4034 1.6072 0.0818 0.1774 1.6072 −0.2661 −0.3117 1.6072 0.2079 0.0873 1.6072 −0.3957 −0.2159 1.6072 0.3340 −0.0029 1.6072 −0.5232 −0.1162 1.6072 0.4602 −0.0931 1.6072 −0.6484 −0.0130 1.6072 0.5865 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0.6814 −0.8490 1.9799 −0.6541 0.7479 1.9799 0.5412 −0.7840 1.9799 −0.5329 0.6526 1.9799 0.3984 −0.7129 1.9799 −0.4116 0.5578 1.9799 0.2582 −0.6375 1.9799 −0.2896 0.4634 1.9799 0.1207 −0.5578 1.9799 −0.1673 0.3698 1.9799 −0.0140 −0.4733 1.9799 −0.0443 0.2770 1.9799 −0.1458 −0.3842 1.9799 0.0793 0.1848 1.9799 −0.2748 −0.2904 1.9799 0.2029 0.0929 1.9799 −0.4015 −0.1927 1.9799 0.3264 0.0008 1.9799 −0.5260 −0.0916 1.9799 0.4496 −0.0917 1.9799 −0.6484 0.0131 1.9799 0.5729 −0.1842 1.9799 −0.7680 0.1208 1.9799 0.6965 −0.2761 1.9799 −0.8847 0.2311 1.9799 0.8206 −0.3674 1.9799 −0.9984 0.3440 1.9799 0.9411 −0.4549 1.9799 −1.1058 0.4553 1.9799 1.0579 −0.5387 1.9799 −1.2072 0.5648 1.9799 1.1711 −0.6186 1.9799 −1.3030 0.6721 1.9799 1.2808 −0.6948 1.9799 −1.3934 0.7771 1.9799 1.3867 −0.7671 1.9799 −1.4784 0.8797 1.9799 1.4890 −0.8359 1.9799 −1.5579 0.9801 1.9799 1.5876 −0.9010 1.9799 −1.6318 1.0782 1.9799 1.6779 −0.9597 1.9799 −1.7009 1.1735 1.9799 1.7601 −1.0124 1.9799 −1.7624 1.2614 1.9799 1.8340 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2.3527 −1.6594 1.6002 2.3527 1.7794 −1.2842 2.3527 −1.5979 1.5463 2.3527 1.7032 −1.2601 2.3527 −1.5279 1.4864 2.3527 1.6170 −1.2323 2.3527 −1.4490 1.4211 2.3527 1.5208 −1.2002 2.3527 −1.3619 1.3497 2.3527 1.4151 −1.1638 2.3527 −1.2707 1.2751 2.3527 1.2999 −1.1223 2.3527 −1.1755 1.1975 2.3527 1.1802 −1.0773 2.3527 −1.0765 1.1164 2.3527 1.0562 −1.0285 2.3527 −0.9738 1.0317 2.3527 0.9281 −0.9754 2.3527 −0.8673 0.9437 2.3527 0.7965 −0.9176 2.3527 −0.7566 0.8526 2.3527 0.6618 −0.8550 2.3527 −0.6419 0.7583 2.3527 0.5243 −0.7868 2.3527 −0.5230 0.6612 2.3527 0.3843 −0.7126 2.3527 −0.4037 0.5644 2.3527 0.2469 −0.6345 2.3527 −0.2840 0.4682 2.3527 0.1121 −0.5522 2.3527 −0.1638 0.3725 2.3527 −0.0200 −0.4656 2.3527 −0.0430 0.2777 2.3527 −0.1490 −0.3743 2.3527 0.0783 0.1834 2.3527 −0.2753 −0.2785 2.3527 0.1998 0.0895 2.3527 −0.3992 −0.1790 2.3527 0.3211 −0.0048 2.3527 −0.5209 −0.0763 2.3527 0.4419 −0.0995 2.3527 −0.6406 0.0298 2.3527 0.5626 −0.1944 2.3527 −0.7577 0.1389 2.3527 0.6836 −0.2891 2.3527 −0.8721 0.2506 2.3527 0.8049 −0.3833 2.3527 −0.9839 0.3648 2.3527 0.9226 −0.4737 2.3527 −1.0900 0.4773 2.3527 1.0368 −0.5603 2.3527 −1.1905 0.5878 2.3527 1.1474 −0.6431 2.3527 −1.2855 0.6960 2.3527 1.2546 −0.7219 2.3527 −1.3749 0.8021 2.3527 1.3582 −0.7968 2.3527 −1.4586 0.9059 2.3527 1.4582 −0.8680 2.3527 −1.5364 1.0075 2.3527 1.5546 −0.9354 2.3527 −1.6087 1.1066 2.3527 1.6433 −0.9963 2.3527 −1.6755 1.2032 2.3527 1.7238 −1.0507 2.3527 −1.7341 1.2923 2.3527 1.7962 −1.0991 2.3527 −1.7863 1.3729 2.3527 1.8602 −1.1415 2.3527 −1.8322 1.4449 2.3527 1.9159 −1.1779 2.3527 −1.8723 1.5141 2.3527 1.9631 −1.2086 2.3527 −1.9035 1.5761 2.3527 2.0036 −1.2348 2.3527 −1.9238 1.6253 2.3527 2.0376 −1.2566 2.3527 −1.9361 1.6661 2.3527 2.0656 −1.2746 2.3527 −1.9413 1.6977 2.3527 2.0880 −1.2890 2.3527 −1.9406 1.7217 2.3527 2.1037 −1.3018 2.3527 −1.9369 1.7345 2.3527 2.1106 −1.3153 2.3527 −1.9327 1.7419 2.3527 2.1124 −1.3278 2.3527 −1.9299 1.7451 2.3527 2.1111 −1.3378 2.3527 −1.9283 1.7466 2.3527 −1.8822 1.8150 3.0985 2.0077 −1.4246 3.0985 −1.8813 1.8156 3.0985 2.0034 −1.4312 3.0985 −1.8795 1.8167 3.0985 1.9959 −1.4385 3.0985 −1.8758 1.8184 3.0985 1.9844 −1.4447 3.0985 −1.8677 1.8201 3.0985 1.9689 −1.4468 3.0985 −1.8549 1.8193 3.0985 1.9486 −1.4416 3.0985 −1.8328 1.8125 3.0985 1.9227 −1.4326 3.0985 −1.8056 1.7986 3.0985 1.8902 −1.4213 3.0985 −1.7715 1.7761 3.0985 1.8509 −1.4075 3.0985 −1.7313 1.7448 3.0985 1.8041 −1.3909 3.0985 −1.6809 1.7020 3.0985 1.7494 −1.3712 3.0985 −1.6237 1.6513 3.0985 1.6849 −1.3475 3.0985 −1.5634 1.5965 3.0985 1.6108 −1.3196 3.0985 −1.4945 1.5360 3.0985 1.5271 −1.2875 3.0985 −1.4172 1.4698 3.0985 1.4339 −1.2506 3.0985 −1.3322 1.3970 3.0985 1.3313 −1.2086 3.0985 −1.2433 1.3207 3.0985 1.2196 −1.1611 3.0985 −1.1507 1.2411 3.0985 1.1038 −1.1100 3.0985 −1.0545 1.1577 3.0985 0.9839 −1.0546 3.0985 −0.9549 1.0705 3.0985 0.8602 −0.9950 3.0985 −0.8519 0.9796 3.0985 0.7332 −0.9309 3.0985 −0.7451 0.8852 3.0985 0.6034 −0.8616 3.0985 −0.6346 0.7873 3.0985 0.4709 −0.7869 3.0985 −0.5201 0.6863 3.0985 0.3362 −0.7062 3.0985 −0.4052 0.5856 3.0985 0.2040 −0.6219 3.0985 −0.2902 0.4851 3.0985 0.0743 −0.5339 3.0985 −0.1747 0.3853 3.0985 −0.0527 −0.4420 3.0985 −0.0586 0.2860 3.0985 −0.1767 −0.3456 3.0985 0.0581 0.1875 3.0985 −0.2979 −0.2453 3.0985 0.1752 0.0895 3.0985 −0.4167 −0.1414 3.0985 0.2921 −0.0088 3.0985 −0.5334 −0.0344 3.0985 0.4086 −0.1076 3.0985 −0.6476 0.0756 3.0985 0.5247 −0.2068 3.0985 −0.7593 0.1880 3.0985 0.6409 −0.3059 3.0985 −0.8685 0.3028 3.0985 0.7572 −0.4049 3.0985 −0.9754 0.4198 3.0985 0.8700 −0.5001 3.0985 −1.0765 0.5349 3.0985 0.9794 −0.5914 3.0985 −1.1724 0.6476 3.0985 1.0853 −0.6790 3.0985 −1.2629 0.7581 3.0985 1.1879 −0.7627 3.0985 −1.3480 0.8659 3.0985 1.2870 −0.8424 3.0985 −1.4276 0.9714 3.0985 1.3827 −0.9183 3.0985 −1.5019 1.0742 3.0985 1.4751 −0.9903 3.0985 −1.5709 1.1743 3.0985 1.5599 −1.0553 3.0985 −1.6346 1.2716 3.0985 1.6371 −1.1137 3.0985 −1.6904 1.3614 3.0985 1.7066 −1.1654 3.0985 −1.7399 1.4427 3.0985 1.7681 −1.2107 3.0985 −1.7835 1.5152 3.0985 1.8217 −1.2495 3.0985 −1.8221 1.5844 3.0985 1.8671 −1.2823 3.0985 −1.8529 1.6458 3.0985 1.9060 −1.3101 3.0985 −1.8739 1.6943 3.0985 1.9388 −1.3335 3.0985 −1.8872 1.7344 3.0985 1.9659 −1.3526 3.0985 −1.8935 1.7655 3.0985 1.9875 −1.3677 3.0985 −1.8940 1.7892 3.0985 2.0032 −1.3806 3.0985 −1.8912 1.8021 3.0985 2.0105 −1.3942 3.0985 −1.8873 1.8096 3.0985 2.0122 −1.4071 3.0985 −1.8846 1.8129 3.0985 2.0106 −1.4173 3.0985 −1.8830 1.8143 3.0985 −1.8420 1.8806 3.8441 1.8942 −1.4885 3.8441 −1.8412 1.8811 3.8441 1.8899 −1.4948 3.8441 −1.8394 1.8822 3.8441 1.8821 −1.5018 3.8441 −1.8355 1.8835 3.8441 1.8703 −1.5072 3.8441 −1.8274 1.8844 3.8441 1.8549 −1.5084 3.8441 −1.8149 1.8822 3.8441 1.8350 −1.5020 3.8441 −1.7938 1.8733 3.8441 1.8096 −1.4922 3.8441 −1.7680 1.8572 3.8441 1.7779 −1.4798 3.8441 −1.7360 1.8325 3.8441 1.7394 −1.4646 3.8441 −1.6980 1.7991 3.8441 1.6937 −1.4463 3.8441 −1.6499 1.7542 3.8441 1.6403 −1.4245 3.8441 −1.5943 1.7026 3.8441 1.5774 −1.3984 3.8441 −1.5345 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1.5828 8.3179 0.8151 −1.4172 8.3179 −1.0265 1.4847 8.3179 0.7201 −1.3316 8.3179 −0.9459 1.3823 8.3179 0.6225 −1.2410 8.3179 −0.8627 1.2752 8.3179 0.5228 −1.1456 8.3179 −0.7769 1.1635 8.3179 0.4211 −1.0449 8.3179 −0.6884 1.0474 8.3179 0.3177 −0.9389 8.3179 −0.5974 0.9267 8.3179 0.2128 −0.8273 8.3179 −0.5036 0.8014 8.3179 0.1067 −0.7099 8.3179 −0.4102 0.6760 8.3179 0.0032 −0.5905 8.3179 −0.3172 0.5502 8.3179 −0.0979 −0.4691 8.3179 −0.2243 0.4243 8.3179 −0.1963 −0.3456 8.3179 −0.1314 0.2984 8.3179 −0.2923 −0.2201 8.3179 −0.0384 0.1727 8.3179 −0.3860 −0.0928 8.3179 0.0551 0.0472 8.3179 −0.4778 0.0359 8.3179 0.1485 −0.0782 8.3179 −0.5678 0.1662 8.3179 0.2417 −0.2039 8.3179 −0.6561 0.2978 8.3179 0.3344 −0.3299 8.3179 −0.7430 0.4307 8.3179 0.4270 −0.4560 8.3179 −0.8283 0.5646 8.3179 0.5193 −0.5823 8.3179 −0.9123 0.6997 8.3179 0.6084 −0.7045 8.3179 −0.9920 0.8314 8.3179 0.6944 −0.8225 8.3179 −1.0676 0.9594 8.3179 0.7774 −0.9362 8.3179 −1.1392 1.0836 8.3179 0.8573 −1.0457 8.3179 −1.2068 1.2039 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9.8092 −1.5417 2.3465 9.8092 1.2783 −1.9967 9.8092 −1.5159 2.3120 9.8092 1.2480 −1.9661 9.8092 −1.4852 2.2677 9.8092 1.2120 −1.9298 9.8092 −1.4461 2.2095 9.8092 1.1699 −1.8869 9.8092 −1.4011 2.1424 9.8092 1.1206 −1.8362 9.8092 −1.3527 2.0710 9.8092 1.0639 −1.7774 9.8092 −1.2980 1.9908 9.8092 1.0000 −1.7103 9.8092 −1.2370 1.9020 9.8092 0.9291 −1.6349 9.8092 −1.1698 1.8043 9.8092 0.8514 −1.5508 9.8092 −1.0994 1.7023 9.8092 0.7671 −1.4581 9.8092 −1.0262 1.5956 9.8092 0.6802 −1.3605 9.8092 −0.9503 1.4842 9.8092 0.5908 −1.2581 9.8092 −0.8719 1.3681 9.8092 0.4990 −1.1506 9.8092 −0.7909 1.2472 9.8092 0.4052 −1.0378 9.8092 −0.7073 1.1215 9.8092 0.3095 −0.9198 9.8092 −0.6211 0.9911 9.8092 0.2121 −0.7963 9.8092 −0.5321 0.8561 9.8092 0.1132 −0.6670 9.8092 −0.4435 0.7209 9.8092 0.0163 −0.5363 9.8092 −0.3550 0.5855 9.8092 −0.0788 −0.4043 9.8092 −0.2666 0.4501 9.8092 −0.1719 −0.2707 9.8092 −0.1780 0.3149 9.8092 −0.2631 −0.1358 9.8092 −0.0893 0.1797 9.8092 −0.3526 0.0004 9.8092 −0.0001 0.0448 9.8092 −0.4408 0.1376 9.8092 0.0892 −0.0900 9.8092 −0.5276 0.2759 9.8092 0.1783 −0.2249 9.8092 −0.6132 0.4150 9.8092 0.2674 −0.3599 9.8092 −0.6975 0.5548 9.8092 0.3564 −0.4949 9.8092 −0.7808 0.6954 9.8092 0.4454 −0.6299 9.8092 −0.8630 0.8366 9.8092 0.5315 −0.7604 9.8092 −0.9413 0.9737 9.8092 0.6147 −0.8862 9.8092 −1.0158 1.1067 9.8092 0.6951 −1.0076 9.8092 −1.0868 1.2355 9.8092 0.7727 −1.1243 9.8092 −1.1542 1.3600 9.8092 0.8475 −1.2364 9.8092 −1.2181 1.4801 9.8092 0.9196 −1.3438 9.8092 −1.2785 1.5960 9.8092 0.9889 −1.4465 9.8092 −1.3353 1.7076 9.8092 1.0524 −1.5402 9.8092 −1.3884 1.8151 9.8092 1.1101 −1.6249 9.8092 −1.4353 1.9133 9.8092 1.1621 −1.7003 9.8092 −1.4763 2.0023 9.8092 1.2081 −1.7668 9.8092 −1.5118 2.0820 9.8092 1.2482 −1.8243 9.8092 −1.5437 2.1572 9.8092 1.2821 −1.8729 9.8092 −1.5703 2.2227 9.8092 1.3113 −1.9143 9.8092 −1.5893 2.2738 9.8092 1.3359 −1.9491 9.8092 −1.6025 2.3153 9.8092 1.3562 −1.9776 9.8092 −1.6101 2.3471 9.8092 1.3724 −2.0005 9.8092 −1.6135 2.3713 9.8092 1.3850 −2.0180 9.8092 −1.6133 2.3850 9.8092 1.3921 −2.0323 9.8092 −1.6112 2.3935 9.8092 1.3921 −2.0457 9.8092 −1.6089 2.3971 9.8092 1.3879 −2.0556 9.8092 −1.6072 2.3985 9.8092 −1.5590 2.4768 10.2860 1.3292 −2.0980 10.2860 −1.5580 2.4773 10.2860 1.3223 −2.1024 10.2860 −1.5558 2.4776 10.2860 1.3116 −2.1049 10.2860 −1.5515 2.4770 10.2860 1.2982 −2.1020 10.2860 −1.5436 2.4731 10.2860 1.2858 −2.0913 10.2860 −1.5331 2.4646 10.2860 1.2708 −2.0752 10.2860 −1.5164 2.4466 10.2860 1.2514 −2.0543 10.2860 −1.4965 2.4209 10.2860 1.2272 −2.0282 10.2860 −1.4720 2.3851 10.2860 1.1978 −1.9964 10.2860 −1.4429 2.3392 10.2860 1.1629 −1.9584 10.2860 −1.4060 2.2790 10.2860 1.1224 −1.9138 10.2860 −1.3634 2.2097 10.2860 1.0747 −1.8609 10.2860 −1.3174 2.1360 10.2860 1.0201 −1.7996 10.2860 −1.2653 2.0533 10.2860 0.9585 −1.7296 10.2860 −1.2070 1.9617 10.2860 0.8902 −1.6510 10.2860 −1.1427 1.8610 10.2860 0.8155 −1.5634 10.2860 −1.0754 1.7558 10.2860 0.7346 −1.4669 10.2860 −1.0054 1.6460 10.2860 0.6511 −1.3654 10.2860 −0.9328 1.5312 10.2860 0.5653 −1.2589 10.2860 −0.8578 1.4116 10.2860 0.4773 −1.1473 10.2860 −0.7804 1.2872 10.2860 0.3872 −1.0304 10.2860 −0.7003 1.1580 10.2860 0.2953 −0.9081 10.2860 −0.6175 1.0240 10.2860 0.2017 −0.7804 10.2860 −0.5322 0.8853 10.2860 0.1065 −0.6470 10.2860 −0.4470 0.7464 10.2860 0.0132 −0.5123 10.2860 −0.3620 0.6075 10.2860 −0.0782 −0.3762 10.2860 −0.2770 0.4685 10.2860 −0.1677 −0.2388 10.2860 −0.1920 0.3297 10.2860 −0.2556 −0.1002 10.2860 −0.1065 0.1910 10.2860 −0.3417 0.0395 10.2860 −0.0207 0.0525 10.2860 −0.4268 0.1802 10.2860 0.0653 −0.0857 10.2860 −0.5106 0.3216 10.2860 0.1514 −0.2240 10.2860 −0.5933 0.4636 10.2860 0.2375 −0.3623 10.2860 −0.6750 0.6062 10.2860 0.3235 −0.5007 10.2860 −0.7557 0.7493 10.2860 0.4095 −0.6390 10.2860 −0.8355 0.8931 10.2860 0.4928 −0.7725 10.2860 −0.9116 1.0325 10.2860 0.5734 −0.9014 10.2860 −0.9841 1.1677 10.2860 0.6515 −1.0255 10.2860 −1.0531 1.2985 10.2860 0.7270 −1.1447 10.2860 −1.1187 1.4249 10.2860 0.8000 −1.2592 10.2860 −1.1810 1.5469 10.2860 0.8705 −1.3687 10.2860 −1.2401 1.6644 10.2860 0.9385 −1.4734 10.2860 −1.2958 1.7775 10.2860 1.0010 −1.5688 10.2860 −1.3477 1.8862 10.2860 1.0579 −1.6548 10.2860 −1.3937 1.9857 10.2860 1.1093 −1.7315 10.2860 −1.4338 2.0758 10.2860 1.1549 −1.7990 10.2860 −1.4683 2.1564 10.2860 1.1946 −1.8573 10.2860 −1.4994 2.2325 10.2860 1.2284 −1.9066 10.2860 −1.5252 2.2988 10.2860 1.2574 −1.9487 10.2860 −1.5435 2.3505 10.2860 1.2819 −1.9838 10.2860 −1.5561 2.3925 10.2860 1.3021 −2.0128 10.2860 −1.5633 2.4245 10.2860 1.3184 −2.0359 10.2860 −1.5663 2.4490 10.2860 1.3308 −2.0537 10.2860 −1.5660 2.4627 10.2860 1.3386 −2.0680 10.2860 −1.5640 2.4712 10.2860 1.3389 −2.0816 10.2860 −1.5616 2.4749 10.2860 1.3346 −2.0917 10.2860 −1.5600 2.4763 10.2860 −1.5248 2.5266 10.5549 1.2922 −2.1064 10.5549 −1.5238 2.5270 10.5549 1.2852 −2.1108 10.5549 −1.5215 2.5272 10.5549 1.2743 −2.1131 10.5549 −1.5172 2.5264 10.5549 1.2611 −2.1098 10.5549 −1.5095 2.5221 10.5549 1.2490 −2.0987 10.5549 −1.4993 2.5131 10.5549 1.2343 −2.0824 10.5549 −1.4832 2.4945 10.5549 1.2152 −2.0612 10.5549 −1.4643 2.4681 10.5549 1.1915 −2.0346 10.5549 −1.4409 2.4313 10.5549 1.1626 −2.0021 10.5549 −1.4133 2.3844 10.5549 1.1285 −1.9635 10.5549 −1.3783 2.3230 10.5549 1.0886 −1.9181 10.5549 −1.3375 2.2523 10.5549 1.0419 −1.8642 10.5549 −1.2935 2.1772 10.5549 0.9883 −1.8017 10.5549 −1.2436 2.0929 10.5549 0.9280 −1.7305 10.5549 −1.1875 1.9996 10.5549 0.8612 −1.6505 10.5549 −1.1255 1.8973 10.5549 0.7882 −1.5614 10.5549 −1.0606 1.7902 10.5549 0.7091 −1.4631 10.5549 −0.9931 1.6784 10.5549 0.6277 −1.3599 10.5549 −0.9231 1.5618 10.5549 0.5439 −1.2515 10.5549 −0.8505 1.4404 10.5549 0.4581 −1.1378 10.5549 −0.7755 1.3140 10.5549 0.3704 −1.0189 10.5549 −0.6980 1.1829 10.5549 0.2808 −0.8946 10.5549 −0.6178 1.0469 10.5549 0.1896 −0.7647 10.5549 −0.5352 0.9062 10.5549 0.0970 −0.6290 10.5549 −0.4526 0.7654 10.5549 0.0062 −0.4922 10.5549 −0.3701 0.6246 10.5549 −0.0828 −0.3540 10.5549 −0.2876 0.4836 10.5549 −0.1698 −0.2146 10.5549 −0.2050 0.3428 10.5549 −0.2553 −0.0738 10.5549 −0.1221 0.2023 10.5549 −0.3392 0.0678 10.5549 −0.0386 0.0619 10.5549 −0.4218 0.2102 10.5549 0.0453 −0.0780 10.5549 −0.5033 0.3532 10.5549 0.1293 −0.2180 10.5549 −0.5837 0.4969 10.5549 0.2135 −0.3579 10.5549 −0.6630 0.6411 10.5549 0.2976 −0.4978 10.5549 −0.7416 0.7857 10.5549 0.3820 −0.6375 10.5549 −0.8192 0.9310 10.5549 0.4638 −0.7724 10.5549 −0.8934 1.0718 10.5549 0.5431 −0.9025 10.5549 −0.9641 1.2082 10.5549 0.6200 −1.0277 10.5549 −1.0314 1.3403 10.5549 0.6945 −1.1479 10.5549 −1.0953 1.4678 10.5549 0.7667 −1.2632 10.5549 −1.1562 1.5908 10.5549 0.8364 −1.3736 10.5549 −1.2139 1.7092 10.5549 0.9038 −1.4791 10.5549 −1.2682 1.8230 10.5549 0.9657 −1.5750 10.5549 −1.3191 1.9326 10.5549 1.0223 −1.6616 10.5549 −1.3638 2.0328 10.5549 1.0733 −1.7387 10.5549 −1.4031 2.1235 10.5549 1.1186 −1.8067 10.5549 −1.4368 2.2045 10.5549 1.1582 −1.8653 10.5549 −1.4672 2.2811 10.5549 1.1919 −1.9149 10.5549 −1.4923 2.3478 10.5549 1.2207 −1.9571 10.5549 −1.5101 2.3998 10.5549 1.2451 −1.9925 10.5549 −1.5223 2.4420 10.5549 1.2653 −2.0215 10.5549 −1.5292 2.4741 10.5549 1.2815 −2.0448 10.5549 −1.5320 2.4986 10.5549 1.2939 −2.0626 10.5549 −1.5317 2.5124 10.5549 1.3016 −2.0769 10.5549 −1.5297 2.5208 10.5549 1.3019 −2.0904 10.5549 −1.5275 2.5245 10.5549 1.2976 −2.1004 10.5549 −1.5258 2.5260 10.5549 −1.4730 2.5996 10.9276 1.2387 −2.1144 10.9276 −1.4720 2.5999 10.9276 1.2315 −2.1186 10.9276 −1.4698 2.6000 10.9276 1.2206 −2.1205 10.9276 −1.4655 2.5989 10.9276 1.2074 −2.1165 10.9276 −1.4583 2.5939 10.9276 1.1958 −2.1048 10.9276 −1.4487 2.5841 10.9276 1.1813 −2.0881 10.9276 −1.4338 2.5646 10.9276 1.1627 −2.0663 10.9276 −1.4162 2.5370 10.9276 1.1395 −2.0392 10.9276 −1.3949 2.4989 10.9276 1.1113 −2.0059 10.9276 −1.3697 2.4505 10.9276 1.0779 −1.9663 10.9276 −1.3377 2.3873 10.9276 1.0392 −1.9197 10.9276 −1.3001 2.3146 10.9276 0.9936 −1.8644 10.9276 −1.2594 2.2372 10.9276 0.9413 −1.8004 10.9276 −1.2129 2.1508 10.9276 0.8826 −1.7273 10.9276 −1.1605 2.0550 10.9276 0.8177 −1.6452 10.9276 −1.1024 1.9499 10.9276 0.7467 −1.5538 10.9276 −1.0414 1.8403 10.9276 0.6698 −1.4530 10.9276 −0.9776 1.7258 10.9276 0.5909 −1.3469 10.9276 −0.9113 1.6066 10.9276 0.5097 −1.2358 10.9276 −0.8425 1.4826 10.9276 0.4267 −1.1193 10.9276 −0.7712 1.3535 10.9276 0.3419 −0.9975 10.9276 −0.6974 1.2197 10.9276 0.2557 −0.8702 10.9276 −0.6212 1.0810 10.9276 0.1680 −0.7372 10.9276 −0.5425 0.9376 10.9276 0.0792 −0.5988 10.9276 −0.4638 0.7939 10.9276 −0.0079 −0.4591 10.9276 −0.3851 0.6504 10.9276 −0.0930 −0.3184 10.9276 −0.3063 0.5068 10.9276 −0.1764 −0.1765 10.9276 −0.2273 0.3635 10.9276 −0.2580 −0.0336 10.9276 −0.1478 0.2203 10.9276 −0.3382 0.1101 10.9276 −0.0677 0.0775 10.9276 −0.4171 0.2547 10.9276 0.0131 −0.0649 10.9276 −0.4948 0.4000 10.9276 0.0943 −0.2070 10.9276 −0.5715 0.5459 10.9276 0.1758 −0.3489 10.9276 −0.6473 0.6922 10.9276 0.2576 −0.4908 10.9276 −0.7222 0.8392 10.9276 0.3399 −0.6324 10.9276 −0.7964 0.9866 10.9276 0.4198 −0.7689 10.9276 −0.8673 1.1294 10.9276 0.4977 −0.9005 10.9276 −0.9349 1.2677 10.9276 0.5731 −1.0270 10.9276 −0.9995 1.4014 10.9276 0.6465 −1.1484 10.9276 −1.0610 1.5306 10.9276 0.7176 −1.2649 10.9276 −1.1194 1.6550 10.9276 0.7864 −1.3763 10.9276 −1.1746 1.7749 10.9276 0.8530 −1.4827 10.9276 −1.2268 1.8901 10.9276 0.9144 −1.5795 10.9276 −1.2756 2.0009 10.9276 0.9704 −1.6667 10.9276 −1.3187 2.1021 10.9276 1.0209 −1.7445 10.9276 −1.3564 2.1936 10.9276 1.0659 −1.8129 10.9276 −1.3887 2.2755 10.9276 1.1052 −1.8720 10.9276 −1.4179 2.3527 10.9276 1.1386 −1.9219 10.9276 −1.4421 2.4199 10.9276 1.1673 −1.9645 10.9276 −1.4591 2.4722 10.9276 1.1916 −2.0000 10.9276 −1.4708 2.5146 10.9276 1.2116 −2.0293 10.9276 −1.4774 2.5469 10.9276 1.2277 −2.0527 10.9276 −1.4801 2.5716 10.9276 1.2401 −2.0707 10.9276 −1.4797 2.5853 10.9276 1.2481 −2.0849 10.9276 −1.4779 2.5939 10.9276 1.2484 −2.0984 10.9276 −1.4757 2.5977 10.9276 1.2443 −2.1084 10.9276 −1.4740 2.5991 10.9276 −1.4319 2.6575 11.2193 1.1968 −2.1207 11.2193 −1.4309 2.6578 11.2193 1.1895 −2.1247 11.2193 −1.4286 2.6578 11.2193 1.1784 −2.1260 11.2193 −1.4245 2.6561 11.2193 1.1655 −2.1210 11.2193 −1.4176 2.6507 11.2193 1.1542 −2.1089 11.2193 −1.4086 2.6403 11.2193 1.1400 −2.0919 11.2193 −1.3947 2.6200 11.2193 1.1216 −2.0699 11.2193 −1.3784 2.5916 11.2193 1.0988 −2.0423 11.2193 −1.3585 2.5526 11.2193 1.0710 −2.0086 11.2193 −1.3352 2.5031 11.2193 1.0383 −1.9683 11.2193 −1.3054 2.4385 11.2193 1.0001 −1.9210 11.2193 −1.2705 2.3642 11.2193 0.9554 −1.8649 11.2193 −1.2324 2.2854 11.2193 0.9043 −1.7999 11.2193 −1.1886 2.1971 11.2193 0.8468 −1.7257 11.2193 −1.1393 2.0994 11.2193 0.7834 −1.6421 11.2193 −1.0843 1.9923 11.2193 0.7142 −1.5492 11.2193 −1.0265 1.8805 11.2193 0.6394 −1.4465 11.2193 −0.9659 1.7640 11.2193 0.5625 −1.3387 11.2193 −0.9027 1.6427 11.2193 0.4837 −1.2257 11.2193 −0.8370 1.5165 11.2193 0.4033 −1.1072 11.2193 −0.7688 1.3855 11.2193 0.3213 −0.9833 11.2193 −0.6981 1.2494 11.2193 0.2377 −0.8538 11.2193 −0.6250 1.1086 11.2193 0.1530 −0.7187 11.2193 −0.5495 0.9628 11.2193 0.0671 −0.5780 11.2193 −0.4739 0.8171 11.2193 −0.0169 −0.4361 11.2193 −0.3982 0.6714 11.2193 −0.0992 −0.2931 11.2193 −0.3224 0.5258 11.2193 −0.1798 −0.1492 11.2193 −0.2460 0.3805 11.2193 −0.2588 −0.0043 11.2193 −0.1692 0.2354 11.2193 −0.3363 0.1415 11.2193 −0.0915 0.0908 11.2193 −0.4124 0.2881 11.2193 −0.0131 −0.0535 11.2193 −0.4875 0.4353 11.2193 0.0660 −0.1973 11.2193 −0.5615 0.5832 11.2193 0.1457 −0.3409 11.2193 −0.6345 0.7316 11.2193 0.2258 −0.4841 11.2193 −0.7068 0.8804 11.2193 0.3065 −0.6271 11.2193 −0.7781 1.0295 11.2193 0.3852 −0.7650 11.2193 −0.8465 1.1740 11.2193 0.4617 −0.8976 11.2193 −0.9119 1.3139 11.2193 0.5362 −1.0252 11.2193 −0.9742 1.4491 11.2193 0.6087 −1.1476 11.2193 −1.0335 1.5796 11.2193 0.6790 −1.2650 11.2193 −1.0899 1.7053 11.2193 0.7471 −1.3773 11.2193 −1.1434 1.8264 11.2193 0.8131 −1.4845 11.2193 −1.1936 1.9427 11.2193 0.8739 −1.5820 11.2193 −1.2407 2.0545 11.2193 0.9295 −1.6698 11.2193 −1.2823 2.1567 11.2193 0.9796 −1.7482 11.2193 −1.3188 2.2489 11.2193 1.0243 −1.8171 11.2193 −1.3501 2.3314 11.2193 1.0632 −1.8767 11.2193 −1.3783 2.4091 11.2193 1.0964 −1.9269 11.2193 −1.4017 2.4769 11.2193 1.1250 −1.9697 11.2193 −1.4183 2.5295 11.2193 1.1491 −2.0056 11.2193 −1.4296 2.5722 11.2193 1.1690 −2.0351 11.2193 −1.4360 2.6046 11.2193 1.1849 −2.0586 11.2193 −1.4386 2.6292 11.2193 1.1973 −2.0767 11.2193 −1.4385 2.6431 11.2193 1.2055 −2.0909 11.2193 −1.4367 2.6516 11.2193 1.2064 −2.1045 11.2193 −1.4346 2.6555 11.2193

It will be appreciated that the airfoil 105 disclosed in the above scalable TABLE 1 may be non-scaled, scaled up, or scaled down geometrically for use in other or similar turbine/compressor designs. Consequently, the coordinate values set forth in TABLE 1 may be non-scaled, scaled upwardly, or scaled downwardly such that the general airfoil profile shape remains unchanged. A scaled version of the coordinates in TABLE 1 would be represented by X, Y, and Z coordinate values of TABLE 1, with the X, Y, and Z non-dimensional coordinate values converted to inches or millimeters (or any suitable dimensional system), multiplied or divided by a constant number. The constant number may be a fraction, decimal fraction, integer or mixed number.

The disclosed airfoil shape thus may increase reliability and may be specific to the machine conditions and specifications. The airfoil shape provides a unique profile to achieve (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade or vane loadings. The disclosed loci of points allow the gas turbine and the compressor or any other suitable turbine/compressor to run in an efficient, safe and smooth manner. As also noted, any scale of the disclosed airfoil may be adopted as long as (1) interaction between other stages in the compressor; (2) aerodynamic efficiency; and (3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled compressor.

The airfoil 105 described herein thus improves overall compressor efficiency. Specifically, the airfoil 105 may provide the desired turbine/compressor efficiency lapse rate (ISO, hot, cold, part load, etc.). The airfoil 105 also meets all aeromechanics, loading and stress requirements.

It should be apparent that the foregoing relates only to certain embodiments of the present application and the resultant patent. Numerous changes and modifications may be made herein by one of ordinary skill in the art without departing from the general spirit and scope of the invention as defined by the following claims and the equivalents thereof. 

We claim:
 1. An article of manufacture having a nominal airfoil profile substantially in accordance with Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete airfoil shape.
 2. The article of manufacture according to claim 1, wherein the article of manufacture comprises an airfoil.
 3. The article of manufacture according to claim 1, wherein the article of manufacture comprises a rotor blade configured for use with a compressor.
 4. The article of manufacture according to claim 1, wherein the airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to an airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to an airfoil surface location.
 5. The article of manufacture according to claim 1, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 6. The article of manufacture according to claim 1, wherein a height of the article of manufacture is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 7. An article of manufacture having a suction-side nominal airfoil profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape, the X, Y, and Z coordinate values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil profile.
 8. The article of manufacture according to claim 7, wherein the article of manufacture comprises an airfoil.
 9. The article of manufacture according to claim 7, wherein the article of manufacture comprises a rotor blade configured for use with a compressor.
 10. The article of manufacture according to claim 7, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 11. The article of manufacture according to claim 7, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 12. The article of manufacture according to claim 7, wherein a height of the article of manufacture is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 13. The article of manufacture according to claim 7, further comprising the article of manufacture having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape, the X, Y, and Z values being scalable as a function of the number to provide at least one of a non-scaled, scaled-up, and scaled-down airfoil.
 14. A compressor comprising a plurality of rotor blades, each of the rotor blades including an airfoil having a suction-side airfoil shape, the airfoil having a nominal profile substantially in accordance with suction-side Cartesian coordinate values of X, Y, and Z set forth in scalable TABLE 1, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by a number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete suction-side airfoil shape.
 15. The compressor according to claim 14, wherein the suction-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a suction-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a suction-side airfoil surface location.
 16. The compressor according to claim 14, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number.
 17. The compressor according to claim 14, wherein a height of each rotor blade is about 1 inch to about 20 inches (about 2.54 centimeters to about 50.8 centimeters).
 18. The compressor according to claim 14, further comprising each of the plurality of rotor blades having a pressure-side nominal airfoil profile substantially in accordance with pressure-side Cartesian coordinate values of X, Y, and Z set forth in the scalable table, wherein the Cartesian coordinate values of X, Y, and Z are non-dimensional values convertible to dimensional distances by multiplying the Cartesian coordinate values of X, Y, and Z by the number, and wherein X and Y are coordinates which, when connected by continuing arcs, define airfoil profile sections at each Z height, the airfoil profile sections at each Z height being joined with one another to form a complete pressure-side airfoil shape.
 19. The compressor according to claim 18, wherein the pressure-side airfoil shape lies in an envelope within at least one of: +/−5% of a chord length in a direction normal to a pressure-side airfoil surface location and +/−0.25 inches (about 6.36 millimeters) in a direction normal to a pressure-side airfoil surface location.
 20. The compressor according to claim 18, wherein the number, used to convert the non-dimensional values to dimensional distances, is at least one of a fraction, a decimal fraction, an integer, and a mixed number. 